Answer: N(20, 4) distribution.
Step-by-step explanation:
Normal approximation to Binomial :
The normal approximation is used for binomial distribution having parameters n and p as
if x is the random variable then x has 
.
Given : As part of a promotion for a new type of cracker, free trial samples are offered to shoppers in a local supermarket.
The probability that a shopper will buy a packet of crackers after tasting the free sample : p=0.20.
Different shoppers can be regarded as independent trials.
if X is the number among the next 100 shoppers who buy a packet of crackers after tasting a free sample.
Then, Mean and standard deviation for x will be :
i.e. X has approximately an N(20, 4) distribution.
A) The equation for circumference is C=2piR. So Filling in for circle A we have 28.26=2*pi*4.5 so we want to isolate pi which I'm gonna call x for it's easier for me xD. So we're gonna start by dividing 4.5 from each side which is gonna leave us with 6.28=2*x which gives you x(pi)= 3.14. For circle B we have 15.70=2*x*2.5 isolate x by first dividing 2.5 which leaves us again with 6.28=2x and x= 3.14.
B) The equation for area is A=piR^2. So again for circle A we have 63.585=x9^2. This one is harder but also are you sure that the area is 63.585 it's supposed to be 254.469 (We'll come back to this)
C) The observation you can make about the value of pi for circles A and B is that it stays consistent at 3.14
Answer:
2.28% probability that a person selected at random will have an IQ of 110 or greater
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean 
and standard deviation 
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
What is the probability that a person selected at random will have an IQ of 110 or greater?
This is 1 subtracted by the pvalue of Z when X = 110. So
has a pvalue of 0.9772
1 - 0.9772 = 0.0228
2.28% probability that a person selected at random will have an IQ of 110 or greater
The triangle is isosceles so m∠A and m∠C are the same.
So to find ∠B, we do 74 + 74 + b = 180
148 + b = 180
b = 180 - 148
b = 32
Answer B is the right choice.
